The green-haired woman in the second season of Tokyo Ghoul was Ginko. She was one of the members of the Corpse Organization and also the classmate of the protagonist, Jin Muyan. At the end of the first season, she was portrayed as a very smart and ambitious character who wanted to become the leader of the ghoul organization. In the second season, she showed a more complicated and dangerous personality and had more connections with Kim Muyan.
It depends on personal preferences. Some people might think Tokyo Ghoul is better for its original story and character development. Others might prefer Tokyo Ghoul:Re for its continuation and new plot twists.
Season 3 of Tokyo Ghoul has a mixed relationship with the manga. While it retains some key elements, it also takes liberties that may not sit well with manga purists. Some story arcs are condensed or altered, affecting the overall coherence compared to the manga.
If you want to know more about the characters in the Tokyo Ghoul, I recommend you to read the novel "The Genius System of Infinite Animation". Its plot includes the main character's role as a search officer in Tokyo Ghoul. You can learn about the characters through the novel. I hope you like this fairy's recommendation. Muah ~π